KABUL — Thirteen Afghan civilians died in violence Sunday as the nation”s hardline vice president expressed hopes for reconciliation and representatives of a militant group with ties to the Taliban brought their own draft of a peace deal to the capital.

Talk of reconciling with insurgents has done little to slow the fighting across Afghanistan, yet the issue is gaining steam, partly fueled by a “peace jirga” that Afghan President Hamid Karzai will host in late April or early May.

The Afghan government and others from the international community have had secret contacts with the Taliban — or their representatives — at the same time that thousands of U.S. and NATO reinforcements are streaming into the country to slow the insurgency.

Helmand province in southern Afghanistan was the scene of Sunday”s deadliest violence. A suicide bomber killed 10 civilians and wounded seven others when he detonated his explosives near an Afghan army patrol at a bridge in Gereshk.

In eastern Afghanistan, two civilians died when a roadside bomb exploded near a crowd celebrating the Afghan new year in Khost province. And in Wardak province, NATO said an elderly man was shot and killed by a joint Afghan-international force that mistakenly believed he was a threat.

Also, NATO said two rockets landed Sunday around the military complex at Kabul airport. A third landed nearby and a fourth hit in the eastern part of the capital. There were no initial reports of casualties.

Besides working on ways to reconcile with the Taliban”s top leaders, the Afghan government is finalizing a plan to use economic incentives to coax low- and midlevel insurgent fighters off the battlefield. Pakistan, Iran and other international players, meanwhile, have begun staking out positions on possible reconciliation negotiations that could mean an endgame to the eight-year-old war.

Harun Zarghun, chief spokesman for Hizb-i-Islami, said a five-member delegation was in Kabul to meet with government officials and also plans to meet with Taliban leaders somewhere in Afghanistan. The group, which has longtime ties to al-Qaida, was founded by Gulbuddin Hekmatyar, a former prime minister and rebel commander in the war against the Soviets in the 1980s.

Spokesmen for the Karzai government could not be reached for comment.

Khalid Farooqi, a member of the parliament from Paktika province, said one delegation from Hizb-i-Islami arrived 10 days ago, and a second one, including Qutbudin Halal, a powerful figure in the group, came on Saturday.

Zarghun, the group”s spokesman in Pakistan, said the delegation is carrying a 15-point plan that calls for foreign forces to start pulling out in July — a full year ahead of President Barack Obama”s desire to start withdrawing U.S. forces in July 2011.

The plan also calls for the current Afghan parliament to serve through December. After that, the parliament would be replaced by an interim government, or shura, which would hold local and national elections within a year, according to the plan. Zarghun said a new Afghan constitution would be written, merging the current version with ones used earlier.

A spokesman for Hekmatyar, Wali Ullah, said Hizb-i-Islami has never refused to join in peace talks, under certain conditions. “The main condition is the empowerment of President Karzai to engage in talks and make decisions,” he said. “The aggressive occupying forces should also announce a schedule for leaving Afghanistan.”

Earlier this month, Hizb-i-Islami fighters battled the Taliban with rocket-propelled grenades and heavy machine guns in Baghlan province. It was not immediately clear whether the clashes were a localized militant dispute or represented signs of a rift between Hekmatyar and the Taliban. But dozens of Hizb-i-Islami fighters, under pressure from the Taliban, ended up joining government forces that had amassed on the edge of the battle zone.

In the northern city of Mazar-i-Sharif to mark the Afghan new year, hard-line Vice President Mohammad Qasim Fahim expressed hope that the upcoming peace jirga will lay a foundation for peace with insurgents.

“The government will try to find a peaceful life for those Afghans who are unhappy,” Fahim, who fought the Soviets and commanded forces that overthrew the Taliban in 2001, told thousands who flocked to a shrine.

Without mentioning the Taliban by name, Fahim said, “God willing, by the help of the people, we will have a successful, historic jirga. … My dear countrymen, my hope is that this year will be the year of peaceful stability.”

Fahim, who has been critical in the past of deals with the Taliban, is an ethnic Tajik and former defense minister, while Karzai and the Taliban leadership are ethnic Pashtuns.

During his speech to the crowd, Balkh provincial Gov. Atta Mohammad Noor also expressed support for reconciliation and stressed the need for input from Afghans across all ethnic factions and regions, especially those who have “been damaged by fighting from both sides.”

Reconciliation cannot set back democracy or women”s rights, he said.

“People without participation of people has no meaning,” Noor said later. “If the people participate or share in this process, then there is no doubt the war machine of the Taliban will get weak.”

Noor said Pakistan appeared to be meddling in possible peace efforts with insurgents when it recently arrested the Taliban”s No. 2 and other members of the insurgency in Pakistan. “The people who were arrested were the people who met with the government,” Noor said.

The U.N.”s former envoy to Afghanistan, Norwegian diplomat Kai Eide, has criticized Pakistan, saying that he and other U.N. officials had been in discussions with senior Taliban officials since last year, but the arrests halted the dialogue. Eide said the Pakistanis surely knew the roles these figures had in efforts to find a political settlement. Pakistan denies the arrests were linked to reconciliation talks.

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Associated Press Writers Zarar Khan in Islamabad, Rahim Faiez in Kabul and Amir Shah in Mazar-i-Sharif contributed to this report.